The period of revolution of planet A around the sun is 8 times that of planet B. How many times the distance…

The period of revolution of planet A around the sun is 8 times that of planet B. How many times the distance of A from the sun is greater than that of B from the sun?
  1. 5 times
  2. 2 times
  3. 3 times
  4. 6 times

Solution

$\begin{aligned} & \left(\frac{\mathrm{R}_1}{\mathrm{R}_2}\right)^3=\left(\frac{\mathrm{T}_1}{\mathrm{~T}_2}\right)^2=(8)^2=64 \\ & \therefore \frac{\mathrm{R}_1}{\mathrm{R}_2}=(64)^{\frac{1}{3}}=4 \\ & \therefore \mathrm{R}_1=4 \mathrm{R}_2 \\ & \therefore \mathrm{R}_1-\mathrm{R}_2=4 \mathrm{R}_2-\mathrm{R}_2=3 \mathrm{R}_2\end{aligned}$

Asked in: MHT CET 2021 (23 Sep Shift 1)

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